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A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications

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Abstract

The system of partial differential equations

$$ \left\{ \begin{array}{l}-{\rm div}(vDu)=f\quad {\rm in}\;{\rm \Omega}\\ |Du|-1=0\quad {\rm in }\;\{v > 0 \} \end{array} \right. $$

arises in the analysis of mathematical models for sandpile growth and in the context of the Monge–Kantorovich optimal mass transport theory. A representation formula for the solutions of a related boundary value problem is here obtained, extending the previous two-dimensional result of the first two authors to arbitrary space dimension. An application to the minimization of integral functionals of the form

$$\int_{{\rm \Omega}} [h(|Du|)-f(x) u]{\rm d}x, $$

with f≥ 0, and h≥ 0 possibly non-convex, is also included.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    P. Cannarsa

  2. UFR des Sciences et Techniques, Université de Bretagne Occidentale, 6 Av. Le Gorgeu, BP 809, 29285, Brest, France

    P. Cardaliaguet

  3. Dipartimento di Matematica, Università di Roma La Sapienza, P.le Aldo Moro 2, 00185, Roma, Italy

    G. Crasta

  4. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    E. Giorgieri

Authors
  1. P. Cannarsa
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  2. P. Cardaliaguet
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  3. G. Crasta
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  4. E. Giorgieri
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Corresponding author

Correspondence to P. Cannarsa.

Additional information

Mathematics Subject Classification: Primary 35C15, 49J10, Secondary 35Q99, 49J30

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Cannarsa, P., Cardaliaguet, P., Crasta, G. et al. A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications. Calc. Var. 24, 431–457 (2005). https://doi.org/10.1007/s00526-005-0328-7

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  • DOI: https://doi.org/10.1007/s00526-005-0328-7

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